1. Field of the Invention
The present invention relates to the quantification of the variability of physiological activity and particularly the quantification of oscillations in physiological response patterns such as the heart rate.
2. Description of the Prior Art
The measurement and determination of effective diagnostic information from the output of physiological response systems (e.g., heart period patterns, peripheral vasomotor activity, electrodermal potentials, electric potentials from the scalp such as EEGs, blood pressure, temperature and all other physiological activity which may be indexed by time) is complicated by the nature of these response patterns which often are characterized by rhythmic oscillations superimposed on an aperiodic baseline. Extremely complex underlying mechanisms of human physiology underlie the mechanisms which produce the signals. That is, physiological response systems tend not to be determined by a single input but are the result of complex interactions of numerous, often undefined, mechanisms. For example, the nervous system has a profound impact on many physiological responses by modifying "homeostatic" oscillations which represent, in particular circumstances, known physiological mechanisms. More specifically, the heart period (the time between successive heart beats) presents oscillations which are located in frequencies common to other physiological response systems. The heart period oscillates at the breathing frequency and at the frequency at which blood pressure and peripheral vasomotor activity also oscillate. The oscillations in the heart period at the "respiratory" frequency and at the "vasomotor" frequency may be interpreted as an indication of specific physiological mechanisms. (See Sayers, "Analysis of Heart Rate Variability", Ergonomics, 1973, Vol. 16, pp. 17-32; and Kitney et al, "Heart Rate Variability in the Assessment of Automatic Diabetic Neuropathy", Automedica, 1982, Vol. 4, pp. 155-167.)
When studying the measured physiological activity in terms of oscillations, the parameters of interest in order to provide information of diagnostic value, include the amplitude of the oscillation, the phase of the oscillation relative to other periodic physiological functions at the same frequency and the coupling or coherence between two or more physiological systems at the same frequency. There are numerous methods used to separate the signals of interest or to detrend physiological data. Many of these on-line devices for monitoring the physiological response systems include high-pass, low-pass or bandpass filters. Other methods include specific statistical analysis which have been developed for engineering and economics applications but which are attempted to be used in regard to the detrending of physiological data. In general, most of these prior art procedures assumed that the trend which is being removed may be characterized by a linear regression or the sum of slow sine waves. While these methods appear to function well in some areas of physiological monitoring including respiration and the electrocardiogram, they are rather limited to those instances where the variance associated with the rhythmic oscillations being studied is large relative to the instability of the baseline upon which these oscillations are superimposed. On the other hand, when the variance associated with the oscillations of interest is extremely small relative to the total variance of the physiological response system, then the above assumptions associated with the previous methods and apparatus of detrending do not apply.
An example of an instance where the prior art type of filtering for purposes of detrending the physiological data fails is that of the amplitude of fetal heart rate oscillations which are very small relative to large changes in the heart rate which have been associated with uterine contractions. This is especially pertinent when a compromised hypoxic fetus exhibits massive heart rate shifts in the baseline in response to the uterine contractions, thus making it very difficult to accurately estimate the amplitude of the fast periodic heart rate activity which is of diagnostic value.
Most of the statistical procedures which are used to assess the characteristics of periodic processes such as the amplitude of rhythmic oscillations involve attempts to detrend the baseline to remove aperiodic components from the data set. These periodic processes which are embedded in the complex signal are attempted to be removed through the use of a sequence involving detrending, filtering, and describing the amplitude and periodicity with spectral analysis such as the fast fourier transform (FFT). The detrending and filtering produces a "processed" signal by removing the aperiodic component which allows for the use of statistical procedures to evaluate the amplitude of the rhythmic oscillations. This "processed" signal is decomposed through the use of spectral analysis and the variance is partitioned into constituent frequencies. That is, the variance is described as the sum of sine waves of various amplitudes and frequencies. The problem with this process is that it may result in faulty interpretations of data if the data set being processed violates specific statistical assumptions necessary for proper interpretation.
Spectral analysis may be used to accurately identify and quantify periodic components in physiological response systems when there are only minute baseline shifts or when the baseline trend can be easily removed prior to analysis. Spectral analysis assumes that the data set being analyzed is weakly stationary. A process is weakly stationary, if its mean and variance are independent of time and its autocovariance function depends only on lag (C. Chatfield, The Analysis of Time Series: Theory and Practice, Chapman and Hall, 1975). Spectral analysis provides reliable and interpretable estimators of the amplitude of a periodic oscillation only if the data are at least weakly stationary.
Another of the unfortunate physiological response system characteristics is that they are not "stationary". This means that physiological response systems are not perfectly sinusoidal and that they have complex shifts in both the mean level and the variance. Thus, by their nature, they violate the assumption of stationarity. Quite obviously then, the spectral analysis to evaluate the amplitude of rhythmic oscillations will result in unreliable estimates of the amplitudes of the rhythmic process at any specific frequency band. By appropriately removing the complex baseline trend, it would be possible for the amplitude of the periodic oscillations to be accurately measured in the filtered data set; however, all of the existing filtering methods and devices which have been used to "detrend" physiological response activity in order to remove the shifting baseline have made faulty assumptions.
Many existing physiological monitoring devices such as polygraphs, electroencephalographs, and electromyographs have hardware filters which function as high-pass, low-pass, or bandpass filters. As previously discussed, this reflects an assumption that there are no aperiodic components in the data and merely that the filters pass the frequency band of interest to the output. Unfortunately, since the data of most physiological systems contain aperiodic trends, the amplitude of the frequencies passed by the various filters will be partially a function of the amount of variance passed through the filters which is, in reality, a portion of the complex aperiodic trend discussed above. Thus, in essence, the hardware filters of prior art devices assume that the baselines are merely the sum of slow sine waves and a linear trend. If the trend is complex and cannot be described by a linear regression or a sum of sine waves with known periodicities and amplitudes, then the sine waves necessary to describe the slow complex trend may include faster periodicities superimposed on the frequencies of interest. Therefore, the operators of the device must know beforehand the shape of the trend to be subtracted from the data set. In the case of spectral analysis, it would be necessary to subtract the spectral densities associated with the trend from the spectral densities associated with the total data set. This is totally impractical because, with the filters being used, the operator would never be able to separate what component of the variance being passed by the filter is associated with the trend from that component of the variance which would be associated with the periodic process. Moreover, it would preclude the ability of the operator to monitor the changing conditions of the periodic physiological process in an on-line operation.
Other methods of operating a filter for removing trends include the use of what is called "successive differencing". This method consists of successively subtracting values through the entire data set involving, for example, the subtraction of data point number 1 from data point number 2 and data number 2 from data point 3, etc. Due to the transfer function of this filter the method may result in an underestimate or overestimate of the spectral densities depending on which frequencies are of interest to the investigator and thus may result in a contamination of the estimates of the variance at any specific frequency. Moreover, the "successive difference" filter is similar to linear detrending and suffers from the same problem of passing variances in higher frequency bands which are components of the aperiodic trend. Other methods include low order polynomial detrending techniques which do not succeed in removing the trend and which also result in an alteration in the shape of the spectrum by influencing both the identification of the peak frequency and the estimate of amplitude at a given frequency.
The clinical and diagnostic value of overcoming the errors brought about by incorrect or simplified assumptions in the prior art devices discussed above can be particularly seen in a specific situation where the amplitude of the oscillation of a physiological process may serve as an indexing variable of a specific underlying mechanism. For example, in the case of heart period, it is possible to interpret the amplitude of the oscillation of heart period at the respiratory frequencies or respiratory sinus arrhythmia (RSA) as an index of the influence of the vagus (10th cranial nerve) on the heart. Briefly stated, the respiratory system transmits afferent information to the brainstem where it "gates" (turns off and on) the vagal efferents to the heart (i.e., vagal efferent activity is reduced during inhalation and reinstated during exhalation). Thus, with regard to heart period oscillations occurring in the respiratory frequencies, the amplitude of such heart period oscillations conveys information regarding the "vagal tone" effect on the heart. With regard to clinical and diagnostic relevance, higher order central nervous system disorders such as intracranial hemorrhage result in a decrease in the vagal efferent influence on the heart. Therefore, the amplitude of the heart period oscillation in the respiratory frequency band (RSA) may provide a "window to the brain" and an early assessment screening of the central nervous system dysfunction.
One of the more important points concerning the relationship exhibited by a fetal heart period is that the heart period pattern exhibits small oscillations at the periodicities associated with breathing in the newborn which frequencies are most likely representative of the RSA in the fetus. Because the periodicities may account for much less than one percent of the total variance of the heart period pattern, the above-discussed points with regard to prior art methods of evaluating and detecting the amplitude of the periodic function become more critical and more prone to error because the percent of variance that the specific periodic function accounts for is extremely small relative to the total variance of the physiological response pattern in the fetal heart period.
In the fetus, the heart period is mainly influenced by the feto-maternal movement and the impact of uterine contractions during labor. Spectral analysis of fetal heart period utilizing any one of the above-discussed filtering techniques would mask the presence of the small oscillations because the percent of variance would be so low that it would not result in a significant or even recognizable peak in the spectrum and because the variance from the complex trends related to either feto-maternal movement or uterine contractions would produce more variance in the frequency band of RSA than the RSA itself.
In summation then, the spectral analysis provides interpretable estimates of the variance (amplitude) on specific frequency bands only when the data do not violate specific assumptions. Most data sets derived from physiological systems such as heart period activity contain aperiodic components and violate the critical assumption of weak stationarity (i.e., the mean and variance are independent of time and the autocovariance function depends only on lag). This is critical when the amplitude of the oscillations of periodic physiological activity conveys critical information regarding the condition of the organism as the instance when the reduction in the amplitude of RSA in the human neonate is associated with brain damage and/or nervous system conditions threatening the viability of the infant. Likewise, spectral analysis and most of the filtering techniques which attempt to remove the trends, are not readily adapted for rapid on-line use.